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I tried with a 593 and had no luck.
I got it aproved instantly online with 600 and two bad marks on CR with $300 limit. After a month they increased it to $1300. It saves 5 cents per gallon on walmart gas.
How long has it been since you asked for the CLI? Did you use the Luv button or did you try the backdoor number and ask by phone? You should receive a letter in the mail from them stating why your request was declined. The letter will show the FICO score and date of the score they used. Most people say, the backdoor phone number is the best way to approach this. They have denied me on the 9th of this month, and the TU report they used, was from July.
I tried using the Luv button too, couldn't get an increase from $150. After 6 months, used the CHAT button in my account section, said I needed $1,000 for a laptop, got an increase to $3,000.